L24 Math 233 Lecture Notes - Lecture 21: Saddle Point, Fxx, Nissan L Engine
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L24 math 233 lecture 21- maxima and minima continued. Maximum and minimum has a tangent line of 0 or no tangent line. Critical points aren"t always maximums or minimums (this is true in one dimension as well) If the second derivative is positive, the function is concave up. If the second derivative is negative, the function is concave down. A saddle point with have one positive and one negative second derivative. D (cid:1249) 0 and and f xx f xx (a, ) (a, ) (cid:1249) 0 (cid:1248) 0 then it"s a local minimum then it"s a local maximum. For d to be positive, f xx and f yy would have to have the same charge as f xy is. D (cid:1248) 0 squared and can only be positive then it"s a saddle point. Then, f xx and f yy would have to have different charges for d to be negative. D=0, then we can not determine what the point is.
